{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 17\n",
    "\n",
    "# 切面\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9726ec9-2cad-44c8-915d-07d8b94fc669",
   "metadata": {},
   "source": [
    "该代码的目的是定义并可视化一个二次函数 $f(x_1, x_2)$ 及其在特定点处的切平面，从而观察该函数的几何特性。其主要包括以下几个部分：\n",
    "\n",
    "### 1. 函数和网格定义\n",
    "首先，代码定义了符号变量 $x_1, x_2, p_1, p_2$，并基于这些变量定义了二次函数：\n",
    "$$\n",
    "f(x_1, x_2) = -4x_1^2 - 4x_2^2\n",
    "$$\n",
    "以及另一个类似的函数 $f(p_1, p_2) = -4p_1^2 - 4p_2^2$。此外，定义了函数 `mesh_circ` 用于生成一个以 $(c_1, c_2)$ 为圆心、半径为 $r$ 的网格，该网格用于后续的可视化。\n",
    "\n",
    "### 2. 梯度和切平面计算\n",
    "接下来，代码计算了 $f(p_1, p_2)$ 在 $p_1$ 和 $p_2$ 的梯度，即：\n",
    "$$\n",
    "\\nabla f = \\left( \\frac{\\partial f}{\\partial p_1}, \\frac{\\partial f}{\\partial p_2} \\right)\n",
    "$$\n",
    "基于这个梯度，构造了函数 $f(x_1, x_2)$ 在点 $(p_1, p_2)$ 处的切平面 $t(x)$：\n",
    "$$\n",
    "t(x) = \\nabla f \\cdot \\begin{bmatrix} x_1 - p_1 \\\\ x_2 - p_2 \\end{bmatrix} + f(p_1, p_2)\n",
    "$$\n",
    "该切平面表示在 $(p_1, p_2)$ 处的线性近似。\n",
    "\n",
    "### 3. 数值化和网格生成\n",
    "代码将 $f(x_1, x_2)$ 和 $t(x)$ 转换为适合数值计算的函数，并生成一个圆形网格 $xx1, xx2$ 用于 $f(x_1, x_2)$ 的可视化。此外，还生成了一个以 $(p_1, p_2)$ 为中心的粗略网格 $(xx1\\_, xx2\\_)$ 用于切平面的可视化。$p_1$ 和 $p_2$ 的值分别设为 $-1.5$ 和 $0$，并在该点计算 $f_x(p_1, p_2)$ 的函数值。\n",
    "\n",
    "### 4. 3D 可视化\n",
    "代码使用 matplotlib 的 3D 绘图库对 $f(x_1, x_2)$ 和 $t(x)$ 进行可视化。首先绘制了 $f(x_1, x_2)$ 的线框图，用灰色显示函数的二次曲面。接着在粗略网格 $(xx1\\_, xx2\\_)$ 上绘制了切平面的线框图，并用红色表示。最后，在 $(p_1, p_2, f_x(p_1, p_2))$ 处标记展开点，以展示二次曲面与其切平面的关系。\n",
    "\n",
    "整体图形设置去除了坐标轴的刻度，仅保留了 $x_1, x_2$ 和 $f(x_1, x_2)$ 的标签，通过适当的视角设置，使 3D 可视化图形更加清晰直观。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b27afbb0-5873-415d-ac6f-7f629f1411c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy  # 导入符号计算库 sympy\n",
    "from sympy import Matrix, Transpose  # 从 sympy 中导入矩阵和转置功能\n",
    "import numpy as np  # 导入数值计算库 numpy\n",
    "from sympy.functions import exp  # 从 sympy.functions 中导入指数函数 exp\n",
    "import matplotlib.pyplot as plt  # 导入绘图库 matplotlib.pyplot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d49b96c5-5355-402f-9f17-b5bf35aacfcf",
   "metadata": {},
   "source": [
    "## 定义自定义函数 mesh_circ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3f5a909c-f8fe-4fb3-a0de-f7a502fc5880",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mesh_circ(c1, c2, r, num):  # 生成圆形网格\n",
    "    theta = np.arange(0, 2 * np.pi + np.pi / num, np.pi / num)  # 生成角度范围\n",
    "    r = np.arange(0, r, r / num)  # 生成半径范围\n",
    "    theta, r = np.meshgrid(theta, r)  # 生成网格\n",
    "    xx1 = np.cos(theta) * r + c1  # 计算 x 轴坐标\n",
    "    xx2 = np.sin(theta) * r + c2  # 计算 y 轴坐标\n",
    "    \n",
    "    return xx1, xx2  # 返回生成的网格"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27add51a-46e7-4093-bc8e-e5add6e2d4dd",
   "metadata": {},
   "source": [
    "## 定义符号变量和函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8152fe44-c471-4d17-ab7b-495c9d56c059",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1, x2, p1, p2 = sympy.symbols('x1 x2 p1 p2')  # 定义符号变量 x1, x2, p1, p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "83e092c2-0a74-49d5-a4d0-2e23c4563b7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 4 x_{1}^{2} - 4 x_{2}^{2}$"
      ],
      "text/plain": [
       "-4*x1**2 - 4*x2**2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x = -4 * x1**2 - 4 * x2**2  # 定义函数 f_x = -4*x1^2 - 4*x2^2\n",
    "f_x  # 打印函数 f_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "47d957a8-6bc8-4291-86ae-ee181e20e794",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 4 p_{1}^{2} - 4 p_{2}^{2}$"
      ],
      "text/plain": [
       "-4*p1**2 - 4*p2**2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_p = -4 * p1**2 - 4 * p2**2  # 定义函数 f_p = -4*p1^2 - 4*p2^2\n",
    "f_p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aad17222-8d85-46be-b812-21441fb3293f",
   "metadata": {},
   "source": [
    "## 计算函数的梯度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7cc7ef78-8ab4-438b-8c5d-4ea38a4b3de4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-8*p1, -8*p2]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_f = [sympy.diff(f_p, var) for var in (p1, p2)]  # 计算函数 f_p 的梯度\n",
    "grad_f  # 打印梯度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f4d62b1c-7151-47d4-835b-4ca6b03642cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_fcn = sympy.lambdify([x1, x2], f_x)  # 将 f_x 转换为 lambda 函数以便数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61414c4d-a442-457f-9333-868ad94ccf0a",
   "metadata": {},
   "source": [
    "## 计算切平面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0836229d-97dd-4684-93d1-eaf7d8f903cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[-4*p1**2 - 8*p1*(-p1 + x1) - 4*p2**2 - 8*p2*(-p2 + x2)]])\n"
     ]
    }
   ],
   "source": [
    "t_x = Matrix(grad_f).T * Matrix([[x1 - p1], [x2 - p2]]) + Matrix([f_p])  # 计算切平面表达式\n",
    "print(t_x)  # 打印切平面表达式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "82e29904-28c1-4208-ba5d-730e409ac419",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_x_fcn = sympy.lambdify([x1, x2, p1, p2], t_x)  # 将切平面表达式转化为 lambda 函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "937de710-7ef3-4faf-a694-59a552a5ba6f",
   "metadata": {},
   "source": [
    "## 将梯度转换为适用于 numpy 的双变量 lambda 函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7ea410e5-41a2-4cbb-bd67-67bc4576ea84",
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_fcn = sympy.lambdify([x1, x2], grad_f)  # 将梯度转化为 lambda 函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae965def-9dbe-445c-9cc2-16ab75db1ea5",
   "metadata": {},
   "source": [
    "## 生成圆形网格"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cf1fd894-aca6-4f1c-8378-fbe0ffaf63ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "xx1, xx2 = mesh_circ(0, 0, 3, 20)  # 生成以 (0, 0) 为圆心、半径为 3 的圆形网格"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "397885a8-c295-4a00-ba8d-bbc0be5bdf45",
   "metadata": {},
   "source": [
    "## 设置展开点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "307fd83a-6589-40b9-916f-521bb6cdc442",
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = -1.5  # 展开点 p1\n",
    "p2 = 0  # 展开点 p2\n",
    "py = f_x_fcn(p1, p2)  # 计算 f_x 在 (p1, p2) 处的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "521749e6-9355-4db3-a56b-08f4b996ef6a",
   "metadata": {},
   "source": [
    "## 生成粗略网格"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a609161f-6eed-4948-911d-3665f4667512",
   "metadata": {},
   "outputs": [],
   "source": [
    "xx1_, xx2_ = np.meshgrid(np.linspace(p1 - 1, p1 + 1, 10),  # 设置 x1 粗略网格\n",
    "                         np.linspace(p2 - 1, p2 + 1, 10))  # 设置 x2 粗略网格"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff60f8e2-dcde-4f30-8208-96d0e9615765",
   "metadata": {},
   "source": [
    "## 计算二次曲面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "79fb8b02-133a-41f6-8dbc-5874f973f977",
   "metadata": {},
   "outputs": [],
   "source": [
    "ff_x = f_x_fcn(xx1, xx2)  # 计算精细网格上的函数值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c1d868c-3e27-4eed-b5bc-8fc949fff6cd",
   "metadata": {},
   "source": [
    "## 计算切平面"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1e3c022b-ac91-44c1-9004-64a250386e4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "tt_x = t_x_fcn(xx1_, xx2_, p1, p2)  # 计算粗略网格上的切平面值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e150bdd-1fa4-4d34-a6cf-d98b3579acd0",
   "metadata": {},
   "source": [
    "## 3D 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bf4e3cc1-f48a-4fae-b3f2-11750cfdfcf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "\n",
    "ax.plot_wireframe(xx1, xx2, ff_x, rstride=1,  # 绘制二次曲面的线框图\n",
    "                  cstride=1, color=[0.5, 0.5, 0.5],  # 设置线框颜色\n",
    "                  linewidth=0.2)  # 设置线框宽度\n",
    "\n",
    "ax.plot_wireframe(xx1_, xx2_, np.squeeze(tt_x), rstride=1,  # 绘制切平面的线框图\n",
    "                  cstride=1, color=[1, 0, 0],  # 设置线框颜色\n",
    "                  linewidth=0.2)  # 设置线框宽度\n",
    "ax.plot(p1, p2, py, 'x')  # 绘制展开点\n",
    "\n",
    "# 去除坐标轴刻度\n",
    "ax.xaxis.set_ticks([])  # 去除 x 轴刻度\n",
    "ax.yaxis.set_ticks([])  # 去除 y 轴刻度\n",
    "ax.zaxis.set_ticks([])  # 去除 z 轴刻度\n",
    "plt.xlim(-3, 3)  # 设置 x 轴范围\n",
    "plt.ylim(-3, 3)  # 设置 y 轴范围\n",
    "ax.view_init(30, -125)  # 设置视角角度\n",
    "ax.set_xlabel('$x_1$')  # 设置 x 轴标签\n",
    "ax.set_ylabel('$x_2$')  # 设置 y 轴标签\n",
    "ax.set_zlabel('$f(x_1,x_2)$')  # 设置 z 轴标签\n",
    "ax.set_proj_type('ortho')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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